We study the sets Ω1,Ω,Σ1andΣ which are associated with a linear mapping preserving a finute dimensional proper cone in wielandt’s approach to Perron-Frobenius theorem.The values of supΩ1,supΩ,infΣ1and inf Σare determined.In case of a nonnegative matrix these values are given in terms of the spectral redii of its classes.Some new results on nonnegative matrix or a singular M-matrix are found.Finally we investiage the question when the peripheral class structure and find some necessary conditions and a sufficient condition.
